We have studied small signal frequency response of a spin laser. We have shown that the response is characterized by two distinct resonant peaks corresponding to the two polarization modes of the spin laser. It is observed that the modulation bandwidth of a spin laser can be smaller or larger than that of a conventional laser depending upon the current bias and spin relaxation time constant. A small value for spin relaxation constant may not be detrimental for modulation bandwidth. This anomalous observation is explained by considering both the amplitude and phase response of the two polarization modes. A spin laser can act as a combination of low-pass and bandpass filters. The passband frequency range is tunable by external bias. We have also studied the evolution of resonant peaks and modulation bandwidth as a function of spin relaxation time constant. (C) 2011 American Institute of Physics. [doi:10.1063/1.3556959]